Our objective is to advance radiological techniques for detection and diagnosis of cancer pathology by developing new algorithms for image reconstruction in computed tomography (CT). The convolution-backprojection algorithm used in conventional CT is applicable to only a few of the possible modes of projection data collection, whereas other scanning modes (e.g., limited field of view, limited range of views) have the potential of reducing the radiation dose to the patient. There are three ways of circumventing the restrictions imposed by the conventional algorithm: (i) Fomulate a general-purpose algorithm capable of reconstructing images from a wide variety of projection-measurement modes; (ii) Formulate a special-purpose algorithm for each scanning mode of interest; (iii) Preprocess the data obtained with an unconventional scanning mode so that it can be subsequently processed by convolution-backprojection or by some other conventional reconstruction algorithm. We have formulated four new reconstruction techniques: one for each of categories (i) and (ii) above, and two of type (iii). We propose to implement each of these four algorithms and evaluate their performance using both simulated and experimental data. Beginning with the basic algorithms as presently formulated, each of them will be extended and refined, guided by the results of the computer experiments and by generalizations suggested by the underlying mathematics. We will compare the performance of the algorithms in categories (ii) and (iii), with each algorithm operating on data sets of its own special type, with the performance of the general-purpose algorithm (i) when applied to the same data sets. For the latter algorithm (i) we will also investigate the possibility of improving the accuracy of images reconstructed with conventional scanning modes by incorporating realistic models of CT data collection (including effects due to beam hardening and to the finite sizes of radiation sources and detectors) within the algorithm itself.